Measurement and Design: Measuring in an interdisciplinary research environment. Symposium 29 April 1993

MEASUREMENT

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MEASURING IN AN ex. INTERDISCIPLINARY RESEARCH ENVIRONMENT TU Delft library

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MEASUREMENT

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NMEASURING IN AN

INTERDISCIPLINARV

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SYMPOSIUM 29 APRIL 1993 ORGANIZEO ANO EOITED BY H. KANIS

C.OVERBEEKE

J.

VERG EEST

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TU Delft

Delft University of Technology

Published and distributed by: Delft University Press Stevinweg 1 2828 CN Delft The Netherlands Telephone +31 15783254 Fax +31 15781661 Acknowledgement

Corrie van der Lelie (cover design and lay-out ofthe book) Carlita Kooman (processing of texts)

Stichting Universiteits Fonds Delft (financial support)

CIP-DATA KONINKLIJKE BIBLIOTHEEK, DEN HAAG H. Kanis, C. Overbeeke, J. Vergeest

Measurement and design, measuring in an interdisciplinary research environment / H. Kanis, C. Overbeeke, J. Verg eest. - Delft: Delft University Press. - 111. - Lit.

ISBN 90-407-1085-6 NUGI926

Subject headings: design, measurement, interdisciplinairity Copyright © 1994 by H. Kanis, C. Overbeeke, J. Vergeest All rights reserved.

No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without permission from the publisher: Delft University Press, Stevinweg 1,2628 CN Delft, The Netherlands. Printed in The Netherlands

Contents

5 Preface

7 Organisers' Note for the Invited Speakers 11 Opening Address

Walle M. Oppedijk van Veen, Dean ofthe Faculty of Industrial Design Engineering

15 Measurement in Design: its Scope and Limits Karel Berka

41 The Social Organisation of Complex Tasks Christian Heath and Paul Luff

83 Measurement and Modelling: an Iterative Approach Henk Stassen

111 Human-Centered Design: Integration with Corporate Processes William Rouse

139 Designers in two Cultures of Measurement: an Attempt at Integration

Hans Dirken 149 Addresses

Preface

This symposium started with inviting four speakers on the basis of a note in which we, as organisers, shortly described the theme of the symposium and its relevance for industrial design

engineering. The speakers each wrote an outline of their intended papers. These outlines were made available to the other speakers in order to promote a mutual tuning of the papers.

The book starts with the above-mentioned note for the invited speakers, followed by the opening address by the Dean of the Faculty of Industrial Design Engineering, professor Walle M. Oppedijk van Veen.

The four papers are authored by:

- professor Karel Berka, the former Czechslovak Academy of Sciences, Prague, Czechia,

- dr Christian Heath and dr Paul Luff, Department of Sociology at the University of Surrey/Cambridge Rank Xerox EuroPARC, UK,

- professor Henk G. Stassen, Faculty of Mechanical Engineering at the Delft University of Technology, the Netherlands, and - dr William B. Rouse, Search Technology, Atlanta, USA. The book concludes with a paper by professor Johan M. Dirken focussing on the integration of the presented views.

We thank all authors for their contribution to the symposium and the publication of this book, in particular professor Dirken who chaired the symposium and who took on the difficult task to integrate diverging approaches.

In addition, we are indebted to the following persons: - Eric Vercouteren for the technical organization,

- Corrie van der Lelie for the cover design and for the lay-out of the book, together with Onno van Nierop,

- Carlita Kooman for patiently updating and formatting texts, and - the secretarial staff of the Faculty.

Finally we thank the Stichting Universiteits Fonds Delft for financially supporting the publication of this book.

H. Kanis C. Overbeeke 1. Vergeest

Symposium: Measurement

&

Design

Measuring in an Interdisciplinary

Research Environment

Introduction

Measurement is at the heart of science as the bridge between obselVer and obselVables. Between and also within different disciplines of scientific research diverse concepts of this bridge may prevail. In physics for example, the notion of measurement has not been 'problemized' explicitly during the greater part of its long-standing history as the distinction between the knower and the known is, at least implicitly, presupposed. In social sciences physical methods are readily used to study human behaviour. However, in this area an on-going discussion takes place on the essential nature of measurement, and more specifically, on the degree of applicability ofphysicallaws to behaviour (cf. Pawson, 1989). Also in technical sciences, measurement is of ten directly borrowed from physics and, as such, taken for granted. This latter borrowing imp lies the conviction that the methods used to study natural phenomena can also be used to study artefacts.

It goes without saying that in a research area such as industrial design engineering, where different disciplines meet, diverging points of view should not remain implicit under penalty of confusion and misunderstanding. Moreover, the elucidation of different theoretical perspectives on measurement may be an appropriate vehicle to enhance the conversion of

multidisciplinarity into interdisciplinarity.

The Faculty of Industrial Design

Engineering, Delft University of

Technology

At the Delft University of Technology, the Faculty of Industrial Design Engineering is the pre-eminent meeting place of

researchers from such diverging areas as mechanical engineering, movement sciences, psychology, computer sciences and physics. The research carried out is focussed on the development and designing of a broad scope of products, ranging from kitchen equipment to medical diagnostic instruments, from bus seats to

limb prostheses and from children's toys to CAD-tools. A common denominator of the actual design activities is that new products are to be produced in large series within industry, the challenge being that, generally, future users and use-conditions are only partially known (Smets, 1992).

Two objects of study can be distinguished. First the interaction between human beings and their environment including all kinds of technical artifacts. Here, human beings may be purchasers of products, but can equally well be users both of everyday products and of professional equipment such as industrial designers operating CAD.

The second field of study concerns the design process itself, especially its structure and methodology as key-factors in the development of new products.

Towards a design science

Design engineering is at the crossroads of the natural sciences and the humanities. This has enormous advantages, if only that our engineers are greatly appreciated by industry. However, this position also has disadvantages. For the greater part our research activities that should resuIt in the establishment of a 'design science', i.e. a technology based on theory, are characterized by descriptive and explorative studies rather than by experimental work to test hypotheses derived from theories. This character of our research comes to the fore in:

• the type of research questions addressed, such as - how do people use products,

- what difficulties are experienced in operating products or systems, and

- which physical and mental capabilities or limitations matter in human-product interaction?

• the variety of techniques, such as questionnaires, tracking eye-movements, anthropometric and virtual reality equipment;

• the type of analysis, which is often explanatory rather than directed at establishing causal relationships.

These characteristics are il1ustrative for the young area of

scientific research. Both the absence of deeply engrained research traditions and the variety of disciplines involved constitute a favourable context for due attention to basic questions. Examples

of such questions are: what do outcomes of measurement and results of analysis mean, or, similarly, what is the meaning of a particular type of measurement scale in view of conceptualor theoretical presuppositions. As measurement itself is based upon the interaction between an 'object' and a 'mIe', attributed meanings may vary since differences between 'objects' may affect the 'mIe'. This happens for example when different subjects give divergent interpretations of the 'same' question. Such a divergence can hardly be avoided when people assess a ubiquitous concept like the usability of prototypes or products, however specific the words to describe such a concept might be. In general, internal references for actions that are seen as

intentional, play a vital role in the interaction of human beings with a (man-made) environment. In an extraneous, observational perspective, interindividual differences may essentially blur the interpretation of (dis)similarities in outcomes of measurement in human involved research.

A symposium on measurement

Against the background outlined above a one-day symposium is being organized with the general theme "Measurement in an Interdisciplinary Research Environment". For this symposium four speakers with an established scientific reputation will be invited. Although it is unfeasible and even undesirable to strictly delineate different themes - actually, it is up to the speakers to chart the area of measurement - it nevertheless appears to be practical to indicate some delimitations.

So, to mention a few topics, the symposium should centre around:

- measurement as a means to generate data (also in a historical perspective );

- the meaning of data c.q. meanings attributed to data;

- the (lack of) correspondence between findings from research and 'reality';

- the way in which measurement depends on presuppositions and theory, with regard to operationalizations and ways of analyzing (what one is looking for);

- personal experienees when the actual use of different measuring techniques gets bogged down in discrepancies.

In short, the symposium should make people reflect on what they are doing as researchers. Moments of reflection are needed by researchers. One of ten starts to use techniques of

time or the opportunity to realize wh at the implied

presuppositions and the consequences of one's actions are. The symposium is meant to offer an opportunity for these reflections.

References

Pawson, R. (1989). A measure lor measures: A manifesto lor empirical sociology. London, UK, Routledge.

Smets, GJ.F. (1992). Integration of technology assessment and humanities at the Department of Industrial Design Engineering. Universiteit en Hogeschool., 38 (aug), 263-270.

Opening Address of the Dean of the

Faculty of Industrial

Design Engineering

Walle M. Oppedijk van Veen

Ladies and gentlemen,

On behalf of the Faculty of Industrial Design Engineering, I want to express my gratitude and appreciation for the fact that so many of you have decided to attend this symposium on Measurement & Design, Measuring in an interdisciplinary research environment

In particular, I we1come our guests and speakers from abroad: prof. Karel Berka from the former Czechoslovakian Academy of Sciences, Prague,

dr. Christian Heath and dr. Paul Luff from the University of Surrey and Cambridge Rank Xerox EuroPARC, UK, and dr. William Rouse from Search Technology, Atlanta, USA. Gentlemen, we are very pleased and honoured that you have found time and opportunity to participate in our symposium. Of course, we also gladly we1come our weU known and distinguished guest: prof. dr. Henk Stassen from the Faculty of Mechanical Engineering, member of the Royal Dutch Academy of Science.

Ladies & gentlemen, these five speakers will present their papers and views on the subject of measurement and design. They have been carefuUy selected by the members of the organizing pro gramme committee consisting of :

Heimrich Kanis Kees Overbeeke Joris Vergeest

In my view, the idea and need for a symposium on the topic of measurement resulted from a feeling of surprise when realizing the consequences of the strong technology push in research, model building, measurement and analysis. For example, the development in the computer technology enables us to speed up

the analysis of very large data matrices. A factor analysis by Thurstone (hefore world war II) took several days: today, it is only a matter of tens of seconds. The computer and increased computational facilities stimulated research and complex numerical model building enormously.

With respect to measurement, only rather recently, an almost similar situation can he observed. Modem registration techniques enable us to collect huge numhers of data.

Three examples of measurement/registration devices which are used in our department are :

1) the eye-movement camera used to registrate the movements of the eyes when reading or when observing or scanning a text or an object,

2) the opto-track which is used in ergonomie research to registrate the movements of for example the fingers, or elbows, and

3) the data-glove whieh is used in perception experiments to measure body movements in a virtual reality.

Nowadays, such devices registrate about 50 observations per second, which equals about 100 to 150 data-items per second, depending on the dimensionality of the original observation. The resulting enormously large data-sets can only he handled and processed by computers with extensive memory capacity. Although data storage and handling creates serious technical and methodological problems, the analysis and interpretation of such large data sets is an even more serious problem. The topic of this symposium, however, is not how to analyse such huge data sets. That again is a matter of analytical techniques and computer technology.

The topic of this symposium addresses the more fundamental question: what is measurement all about, what is its use and why do we measure the way we do, particularly in an interdisciplinary environment like Industrial Design Engineering?

The speakers will address these questions from various points of view. In order to give you some idea of the content of their presentations, I will briefly, just very briefly summarize the summaries of the organizing committee and speakers.

1. There is a measurement theoretical presentation, dealing with the contribution of data measurement in product design. The general problems of measurement will he reviewed and the aggregation of data from quite different origins (economie,

aesthetic, anthropometric, mechanical, psychological data) is discussed.

2. There is a presentation dealing with the issue of qualitative or non-numeri cal data (also called non-conventional measurement) as a way to analyse human conduct and to develop product requirements. According to the authors it is primarily concerned with explicating the tacit, common sense knowledge and

reasoning which underlies social action and activity. Examples will be shown of human-computer interaction and technologically mediated interpersonal communication.

3. There is a presentation dealing with the model-building approach, which may be characterized by the slogan: DATA IS KNOWLEDGE or differently, no knowledge without data. More in particular, it deals with the measurement and modelling of complex dynamic environments. It is planned to show that real world problems are dynamic and that system theory is the best basis and general common language to measuring and modelling.

4. Finally, the fourth presentation is from a researcher who has stated elsewhere that research findings (in particular ergonomie measurement data) quite of ten do not meet the designers needs and problems. The presentation today deals with human centred design, as a process of assuring the concerns, values and

perception of all stakeholders in the design process. Case studies are presented to illustrate the use of the appropriate methods and tools to achieve successful innovations.

Ladies and gentlemen, we have a truly interesting pro gramme indeed, and lamsure you will have ample opportunity to participate in an interesting and stimulating debate on

Measurement and Design, coached by the firm but caring hand of prof. Hans Dirken of our faculty. Ladies and gentlemen, the symposium is yours.

Measurement in Design: lts Scope

and Limits

Karel Berka

PART I

To speak about measurement in design does not imply, as I assume, "the form of a copious review of a work on Chinese metaphysics" which was a combination of information obtained in the Encyclopaedia Britannica by reading "for metaphysics under the letter M, and for China under the letter C", as we are told by Ch. Dickens in his Pickwick Papers.

Such an approach is beyond consideration because measurement is a method used by designers in different occasions of their manifold activities. There is, of course, a notabie distinction between a working designer who is actually using measuring procedures or is assuming that he does so without thinking about the theory and methodology of measurement, and a

measurement theorist who has only a very superficial awareness about the ways how designing is really performed.

This is due to two reasons. On one side, there is a natural distrust of practitioners towards theoretical and methodological problems. Such investigations seem to burden their empirically oriented work by unnecessary speculations. On the other one, there is a rather unlimited extent of designing which includes domains of building, constructing and producing, especially various branches of engineering, architecture, electronics, plant design, fashion, art etc. In fact, we encounter designing everywhere insofar man creates artefacts not previously existent in nature, but even in nature itself when changing and modifying his natural

environment. This broad nature of designing is approvingly agreed upon by many authors.

The second stage in decision making is to devise or discover possible courses of actions. This is the activity that in fields like engineering and architecture is called 'design' (Simon,1977, p. 160).

Designing is understood as a component of "an organized system of diverse and independent activities such as decision making, evaluating, cognitive and proposal formulating activities" (Tondl, 1990, p. 620).

This all-embracing scope of design has been wittily characterized by Frank Dudas: "Everything that doesn't happen by accident, happens by design" (Vazquez & Margain, 1980, p. 309). What really happened by accident, in the case of this paper, is the selection of books dealing with problems of measurement in design available in our libraries. Whether the publications quoted are up-to-date and representative enough for a survey of views on this issue, I dare not to assess. I can only hope that they will serve as an acceptable background for my attempt to elucidate the theoretical and methodological problems of measurement in design. Some quotations in which designers are expressing their views will again serve as a starting point:

"Objective measurements - measurements in which performances are recorded in quantitative terms - are strongly preferred to subjective opinions, comments and ratings ... Perhaps the most basic problem in any evaluations of a system is the criterion problem. This is the problem of what to measure" (Morgan et al.,

1963, p. 48).

"Since what I have called rational abstraction in art is measurable and resolves into numericallaws, it is obvious that the machine, which works to adjustment and measure, can produce such work with unfailing and unrivalled precision" (Read, 1934, p. 57). "No instrument has yet been designed to measure Joe's and Josephine's colour reaction" (Dreyfuss, 1955, p. 37).

"Measurement. This is a neutral activity in which the

performance of the model is obtained on as wide a variety of counts as necessary. Costs, environmental conditions, flexibility, space utilization and ergonomie effe cts are among those that suggest themselves easily. Aspects of performance whose measure is a human response, e.g. value judgments of the qualities of an object, can sometimes be obtained from simulation" (Mitchel, 1977, p. 476).

"Loading determination involves the identification and measurement of relevant parameters and the use of this information to estimate total forces on the system" (Haugen, 1980, p. 78).

16

---"Dur participation in professional societies and at conferences ( ... ) is essential for each of us, so that we can continually re-evaluate our professional standards and take participation and direction from our fellow designers who present papers. Even a banal paper serves as a measurement device" (Vazquez & Margain, 1980, p. 311).

"These formal evaluations tend to require that measurement of pertinent parameters prior to introducing the system into a large user community that is different from the original prototype environment. Then after the system is made available in the new setting, careful observation and measurement are required to determine the system's impact" (Hayes-Roth et al., 1983, p. 260).

These quotations sufficiently show the variety of opinions being rather far from an agreement and scarcely reflecting a conceptual clarity. lam sure, for a selection of other texts the heterogeinity will be obvious as weIl. It seems to be justified to point out some explicit or implicit conclusions.

First, there prevails a universal claim to measure practically everything and anywhere without any limits.

Second, there is made no distinction between various kinds of measurement, namely between physical measurement, e.g. of production means, ergometrical procedures, anthropometric techniques or human-body measurements, and various kinds of extraphysical measurement used in behavioural and social

sciences, e.g. of consumers attitudes, their expectations, wishes or desires, the utility of designed products, their aesthetic or ethical values.

Third, there the difference between measuring tools of physical measurement is neglected, i.e. various technical instruments, e.g. a balance weight, a sonar, and those of extraphysical measurement, i.e. various conceptual devices, e.g. questionnaires, interviews.

In order to elucidate these topics a survey of general problems in measurement theory and methodology will be useful. I hope that designers themselves will accept this approach as a desirabIe supplement and not as an unnecessary speculation without practical impacts.

PART 11

2.1 A survey of general problems

Measurement as any other human activity does not exist without some presuppositions, and its exposition is natura1ly influenced by subjective views of the interpreter. My presentation will be based on my previous work in this field, and will be inevitably

determined by its positive and negative features (Berka, 1983, 1983a, 1992).

2.2 Measurement theory

The present situation in measurement theory is affected by the alluring prospect of mathematization considered as the paradigm of exactness and rigour in science. It is rooted in the very beginnings of science and philosophy with Pythagoras and Plato. This tendency has been reinforced in the rise of modem science by the convincing results obtained in mathematical physics. It was, in fact, proc1aimed by Galileo's programme "to measure what is measurable and to try to render measurable what is not so yet". This development being a revival of the platonic ideal of universal mathematization, has in this century spread into various branches of behavioural and social sciences and has affected even humanities.

The utilization of measuring procedures also in psychology and education, later on in sociology opened the discussion about the relationship between qualitative and quantitative aspects of entities, the possibility to measure outside its previous domains and other theoretical topics. Is the transfer of measurement appropriate at all? Are there not some constraints which deserve a modification? Are there identical or at least similar conditions of measurement used in physics, e.g. in the case of length, and when applied in psychology attempting to measure e.g. taste or pain? Can we fmd a theoretically justified and practically satisfactory definition of the measurement concept?

Some preliminary answers can be found already in the stand-point of Aristotle towards Plato. According to Aristotle sciences differ by their subject-matter and methods: "We cannot in demonstrating", he says in Analytica Posteriora, "pass from one genus to another. We cannot for instance, prove geometrical truths by arithmetic". Any transfer of methods requires a modification appropriate to the domain in question. For similar reasons, as Aristotle holds in his Metaphysics, we cannot everywhere require the exact mathematical exposition.

Modem critics accused Aristotelian science for its qualitative, purely descriptive, non-experimental character, and that it ignored the relevance of measurement. Aristotelian qualitativism was determined by the fact that the paradigm of scientific enterprise was based on biology and not on physics. Hence the necessity to measure was not so pressing. And Aristotle did not measure, because he had no technical instruments, e.g., no thermometer; for this reason he scarcely could develop a

quantitative conceptual apparatus. In zoology and botanics, at the beginning of these sciences, his qualitative approach was fruitful. Contrary to it, in physics it was evidently harmful.

The present opinions conceming the nature and applicability of measurement will vary because of divergent phiIosophical

convictions or due to various kinds of resuits achieved in different domains.

In principle, there are two opposing conceptions: the broader and the narrower views, the so-called conservative and liberal

conceptions. The former is modelled on measurement in natural sciences and technology, in short, on physical measurement. The Iatter one is defended by scientists working in behavioural and social sciences and amounts to various kinds of extraphysical measurement.

According to the broader view advocated e.g. by S.S. Stevens, measurement is understood as the assignment of numerals to objects or events according to rules. The narrower view is reflected by the representational theory according to which measurement is a homomorphic mapping of some empirical reiational system onto a definite numeri cal relational system, respectiveIy, an assignment of numbers to things in such a way that operations on and relations among the numbers assigned rep re sent corresponding empirical operations and relations. I personally defend a variant of the representational theory which is based of correspondence rules only and exc1udes special axioma tic systems constructed in order to formulate under what conditions measurement would be possibie. I hold that

measurement is appropriate only for the assignment of numbers of empirical properties, but not for numerals. What is, therefore, relevant, is to find empirical counterparts to operations and relations of the numerical system. This requirement can be secured by correspondence rules, e.g.

where the left side is a numerical expres sion and the right one expresses the empirical relation of precedence or succession. These mIes correlate empirical properties of measured objects to forma! properties of numbers. The most important

correspondence rule a + b = c <==> (xSy)Kz

correlates the numerical operation of addition with the empirica! operation of concatenation, namely "x connected (combined, concatenated) with y coincides with z".

There is no need to construct special axiomatic systems, as is done by adherents of the formalistic stand-point in the philosophy of measurement. This task is redundant, because there have been long ago constructed well grounded axiomatic systems in number theory. Further, what makes measurement really vaIuable is its realization in practice and not speculations under what conditions it wouid be possibie.

It seems that this modified approach to the representational theory does not satisfy proponents of the broader view. So e.g. Schwager (1988, p. 159) remarks: "Representational theory can stand on dogmatic purity and condemn non-representational measurement; in that case it rejects the Iargest share of

measurement in the social sciences". Answering this point of view I shall but raise the following question: Is measurement really so important for the prestige and scientific status of social sciences? The assignment of numbers to empirical properties is - according to the ontological standpoint in the philosophy of measurement -significant only if it refers directly or in a mediated manner to quantitative aspects of empiricalobjects. A purely qualitative property which cannot be brought into any relationship with some quantitative aspect is not measurable in the strict sense of this term. Seen from the narrower point of view, it is not possible to change the ontological status of a property simply by adopting some measurement procedure or by assigning numerals to it, as it is supposed by advocates of operationalism. Neither can this be achieved by conventions based on human agreement or by considerations of simplicity according to the instrumentalist stand-point. I assume that the formalistic stand-point is equally weU misleading.

In accordance with the realist's stand-point (Beyerly & Lazara, 1973), or rather in a more explicit version I assume for a safe grounding of measurement the following suppositions: (i) measurement has an objective ontological foundation; (ii) quantities, or rather quantitative aspects of empiricalobjects exist independently and prior to any measurements;

(iii) magnitudes are historically determined reflections of quantitative aspects of objectively existing entities.

By adopting an opposite view, an anti-ontological stand-point to the foundational problems of measurement, the scope of this procedure could be extended without any reasonable limits. No historically determined boundary not even a relative one -would exist between what can be and what cannot be measured. Any operation connected with the assignment of numerals could be labelled as measurement. The restriction "according to mIes" is, in fact, without any constraints because such mIes are agreed "by fiat". I have, of course, to admit that this view restricts the scope of extraphysical measurement.

I think that we cannot equate physical and extraphysical

measurements: there exist beside some common features serious differences. This insight is reflected especially by the following distinctions:

(i) physical measurement utilizes various technical means and devices; extraphysical measurement depends on nontechnical devices - tests, questionnaires, interviews;

(ii) physical measurement is closely connected with systems of magnitudes, measurement units and dimensional analysis. The absence of a system of extraphysical magnitudes and

measurement units is - so to say - compensated by such issues as meaningfulness, validity and reliability.

I do not, of course, hold that magnitudes in physics are absolutely independent on measuring procedures or measuring instmments used. The existence of various procedures used in the

measurement of one magnitude is not a matter of arbitrary choice. It rests upon objective grounds, theoretical considerations and practical reasons. In order to measure a magnitude in its whole extent, there have been developed and utilized different operations, various measurement tools. For example, we cannot measure "very small" or "very large" values of the magnitude "length" by the measuring rod.

2.3 Quantification

Neither science nor technology nor any other field of human practice is interested in measurement in itself. The endeavour to obtain quantitative data serves various goals: to formulate quantitative laws; to confirm, verify of falsify a hypothesis or a theory; to support some project, decision, design, by objectively characterized data, by intersubjectively acknowledged items. Contemporary views on quantification - understood in a very broad sense - are related with the distinction of four different kinds: numbering and scaling, counting and measurement. According to my view only counting and measurement can be considered as kinds of quantification in the strict sense of this term. Only in these two cases the numerals assigned to empirical objects are names of numbers and not simply special signs which principally fulfill the same function as other signs - letters, words, etc. For numbering, this stand-point is accepted today by the majority of measurement theorists. But in the case of scaling which is understood again in a broader and narrower sense, there is no such an agreement.

2.3.1 Numbering or numerization is used to designate or name

something. Such numeri cal naming of individual objects or of sets of objects, e.g. of convicts, prisoners of war, streets, houses, passports, identification cards etc. has evidently its merits: it is easy to survey, it enables a quick orientation and an

unproblematic enlargement of such labels. There is, of course, a latent danger: the numerals used do not designate numbers, they do not refer to objectively existing quantitative aspects of objects. I propose, therefore, in this case to speak about

pseudo-quantification.

2.3.2 Neither scaling, understood in the narrower sense, i.e. restricted to rank ordering, fulfills the basic condition of quantification: it does not yield quantitative data expressed by means of cardinal numbers. The numerals used inform us whether some property of some object does or does not oecur in a greater or lesser degree than in another one, but they do not give any information as to the amount in which one object excels another one. They do not answer the question "how much?". Sealing restricted to rank orde ring only is an instance of quasi-quantifieation.

Rank ordering is a presupposition of measurement: it is a fruitful kind of evaluating preferences by taking advantage of the serial property of ordinal numbers whieh many people will con si der

more obvious than such comparative terms as "better" , "much better", "much more better" etc.

2.3.3 Counting enables us to find out the amount of elements in some set of discrete, welI-discemible individual objects. When the counted objects are not unambiguously discemible, e.g. when counting grains of salt which are differentiated only with difficulty or poems with highly aesthetic impacts, since in this case the determination of such poems depends on additional rather subjective criteria which are different from man to man, the results of this procedure are not exactly determined.

Counting presupposes that the objects counted occur in a temporal succes sion or if they appear simultaneously that we can register them gradually. Counting does not assume a

homogeneity of the elements of the set whose numerosity we want to find out. Thus we obtain basic quantitative data

mathematically expressed by non-negative whole numbers which can refer to objects which are in respect to their properties very -may be extremely - different. This fact constraints the fruitfulness of an unlimited application of this procedure.

2.3.4 Measurement as an empirico-mathematical procedure

presupposes - in the strict sense - a measurement unit and a scale zero, a naturalor an arbitrary origin. Contrary to it, for counting the assumption of a scale zero is absurd, and the adoption of a unit of counting, i.e. an unnamed non-negative whole number 1, is trivia!.

What is then the relation between both instances of quantification proper: counting, e.g. the numerosity of a flock of sheep, and measuring, e.g. the length of a fence? Beside the view of their relative independence, there are two opposing reductionistic opinions: some methodologists consider counting as a special kind of measurement, especially when regarding number or

numerosity as a metrical magnitude; contrary to it, others reduce measurement to counting, namely of the number of measurement units included in the measured magnitude.

The distinction of pseudo-, quasi- and quantification proper corresponds to the classification of concepts into classificational (qualitative), e.g. 'long', topological (comparative), e.g. 'longer than', 'as long as', and metrical (quantitative), e.g. '5 m long'. It is, at the same time, connected with topologization and metrization, with topological and metrical conditions of measurement.

Metrization is a conceptual procedure, a theoretica! background of measurement. In addition to their common formal structure, measurement depends on its practical results: on the actually achieved numeri cal values with a relevant empirical

interpretation.

According to the representational theory, there are two basic problems of metrization which have to be positively solved. The problem of representation concerns the mapping of an empirical relational system onto a numerical relational system, and in order to draw from numerical statements empirically relevant

conclusions it requires for numerical relations and operations corresponding empirical counterparts. The problem of uniqueness consists in the establishment of permissible transformations under which the numerical values obtained are uniquely determined. This problem is thus determined by transformations under which the numerical values obtained by measurement are invariant. Metrization is realized in two steps: as topologization and metrization proper. Topologization is, at the same time, related with rank-ordering. lts structure is determined by the numerical calculus of weak ordering, based on two primitive arithmetic notions: "<" and "=". Metrization is characterized by the

restricted additivity calculus limited to positive real numbers and based (in addition to the primitive concepts of topologization) on the notion of addition (cf. for details e.g. Berka, 1983, p. 133 ft). 2.4 Theory of scales

Starting with the work of S.S. Stevens, a homomorphism from empirical relational structures onto numeri cal relation structures has been called a scale, more precisely a conceptual scale, in distinction of a material scale which is understood as a

component of some measurement instrument (Bunge, 1967, p. 221). There are usually distinguished four basic, hierarchically ordered scale types:

(i) The nominal scale is determined by the operation

"determination of equality", i.e., the rule "do not assign the same numeral to different classes or different numerals to the same class", and the permutation group; it is invariant under a one-to-one substitution. This scale type is exemplified e.g. by numbering of football players.

(ii) The ordinal scale is in addition to the nominal scale operation determined by the relation "determination of greater or less" and by the isotonic, i.e. order preserving group; it is invariant under every monotonic transformation. The usual examples of this scale

---

---type are the Beaufort's scale of wind force or the Moh's scale of hardness.

(iii) The inteIVal scale extends the empirical operations so far introduced by the "determination of the equality of inteIVals or differences" and from the mathematical point of view it is determined by the generallinear group x'

=

ax +

P

(<DO), where a has to be understood as the measurement unit and

p

as the scale zero. This scale type is invariant in respect to any positive linear transformation; it is usually exemplified by

measurements of temperature in Celsius, Réaumur or Fahrenheit degrees.

(iv) The ratio scale, the most powerful scale type, assumes as an additional empirical operation the "determination of equality or inequality of ratios", and in respect to its formal properties it is characterized by the similarity group x' = ax (<DO), where a denotes the measurement unit. This scale type is an inteIVal scale with a natural scale zero, hen ce the constant

P

is redundant. The ratio scale is invariant to every similarity transformation, and it can be used in all measurements of magnitudes with an empirical concatenation operation, e.g. length measurement. Because of its arithmetical counterpart - the operation of addition - the scale values can be expressed by rational numbers, or due to extrapolation by computation by real numbers as weU.

Comparing the above mentioned types of quantification with the theory of scales, the foUowing correlations are obvious:

(i) pseudo-quantification and nominal scales, (ii) quasi-quantification and ordinal scales, and (iii) quasi-quantification and inteIVal and ratio scales.

Taking into account the difference between scaling and

measurement determined by the distinction of topologization and metrization, it is possible - if starting with the theory of scales - to distinguish scaling scales and measurement scales, respectively topological scales, i.e. ordinal scales, and metrical scales, i.e. inteIVal and ratio scales.

2.5 Scale origin and measurement units

The scale origin and the measurement unit inherent to metrical scales are subject-matter of discussion centred on questions of arbitrariness, objectivity, conventionality and ontological dependency.

Some authors overestimate the distinction of "naturaI" or "absolute" and "arbitrary" scale origins, as a rule exemplified by the difference between two types of temperature scales: the

Celsius, Réaumur or Fahrenheit as instances of interval scales and Kelvin or Rankine as instances of ratio scales.

According to my opinion, both scale zeros are objectively determined and as theoretical constructs they are neither absolutely arbitrary nor absolutely natural. In the first case we dispose, of course, of a variety of more than one choice; hence, the absolute zero has a less conventional character than the arbitrary zero. The difference between these two scale origins is only a matter of degree.

Similarly, it seems to be misleading when one speaks about the conventional nature of the measurement unit, unless we make it quite cIear that the conventions adopted by selecting various unit systems are not arbitrary at all. It is true, we can select various units used in measurement of one magnitude, but this choice has never been made without reason, though today, some

measurement units, e.g. a scruple when measuring weight, or a perch in the case of length measurement, may not seem to be very sound or convincing from the theoretical or practical viewpoint. The selection of units "is an expression of a condensed human practice, theoretical considerations and a very diligent process of standardization. In the choice of measurement units, conventionality refers not to their qualitative, but only to their strictly quantitative aspects: only the size of basic measurement units is conventionally selected" (Berka, 1983, p. 63).

Were the choice ofmeasurement units really conventional, i.e. simply determined by human will or by agreement among people, then it could make no difficulty to introduce units for measuring various assumed measurable magnitudes in

behavioural and social sciences, e.g. intelligence quotient, utility, work attitude, student achievements etc. The lack of units in these fields is a convincing counter-example for all those who suppose that measurement units can be conventionally selected.

It yields, at the same time, enough evidence against the anti-ontological stand-point of operationalism or instrumentalism in the philosophical foundations of measurement. Analogously, the lack of operationally realizable units is also a strong argument against the formalist stand-point. Such an absence cannot he compensated by complicated axiomatizations. Scientists and technicians are not interested in the hypothetical assumption under what conditions measurement would be possible, but primarily whether some property is measurable at all and under what empirically feasible conditions. To find an empirical

counterpart of numerical operations and relations is a sufficient condition in order to speak about the assignment of numbers to properties of objects to be measured. And this task can be achieved by correspondence ruies which will immediately characterize the very nature of the measured objects.

Correspondence mIes of topoIogization will indicate that we have to do - naturally when empirically realized - with ordinal scaie values, hence with non-metrical magnitudes. Similarly,

correspondence mIes of metrization will express the fact that the measurement will result with the assignment of cardinal scale values.

2.6 Some methodological problems

For a fmitful application of concrete measurement procedures various methodological problems des erve an appropriate attention. I shall confine my exposition to two issues only: (i) to the distinction of primary and secondary measurements which is primarily relevant for physical measurement, and (ii) to the problems of meaningfuiness, validity and reliability which are important in the domain of extraphysical measurement. The distinction of primary and secondary me as ure ment is

equivalently expressed by the difference of fundamental and derived measurement as weIl. This distinction is closely connected with classifications of metrical magnitudes and with systems of magnitudes and their units in physics.

For primary or fundamental measurement, there exists an imrnediate and direct empirical interpretation of the basic

numerical concepts, namely "greater or less", "equal" and "plus". This operationalization is prior to and independent of any

previous measurements. Fundamentally measurable metric magnitudes are then considered as the basis for elaborating systems of physical magnitudes, for systems or measurement units, e.g. for the seven-dimensional system - meter, kilogram, second, Kelvin etc. (the SI measurement system).

On the basis of fundamental magnitudes all other metrical magnitudes are obtained by means of physicallaws. Metrical magnitudes which are not fundamentally measured are obtained by derived or secondary measurement which is a combination of fundamental measurement and calculation. A classical example is the measurement of length and mass.

The differentiation of primary and secondary measurement is not exhaustive. If one measures, e.g. temperature, it will be possibie

to measure pressure or volume or electric resistance or another one of the many thermometric characteristics. For certain derived magnitudes special instruments have been constructed by means of which such magnitudes can be measured directly, i.e.

fundamentally, e.g. the density of a liquid can be measured by a hydrometer.

In the domain of extraphysical measurement other kinds have been advocated as well. The most important role is ascribed to associative or conjoint measurement.

The associative measurement is based on an independently measured fundamental or derived magnitude and its lawlike association with some other magnitude. This correlation is used as a device for drawing consequences conceming numerical

properties of directly not measurable magnitudes. According to B. Ellis (1966, p. 54t), associative measurement is used even in physics, e.g. in temperature measurement, since in this case we directly measure only the length of some thermometric stuff. Conjoint measurement - either additive or polynomial- is intensively studied in formal representational theories (comp. Krantz et al., 1971). It is concemed with the measurement of composite objects by means of independent, simultaneous measurement of its components in respect to relevant attributes, whereby the scale values of the composite object are a function of the scale value of these components, e.g. preference or comfort. Advocates of this conception have attempted to reveal the metrization conditions rather than convincingly shown the practical utilization of conjoint measurement.

The problems of meaningfulness, validity and reliability are indeed conceived even as the theoretical core of extraphysical measurement, they are urgent also for designers:

(i) "The most important theory of measurement in social science is the rather loose set of practices assembied around the concept ofvalidity and reliability." (Schwager, 1988, p. 29).

(ii) "In the social sciences, especially psychology and education but also sociology and political science, the problems of the adequacy of measurement are frequently discussed under the headings of "validity" and "reliability". It is probably no exaggeration to claim that the overwhelming majority of psychological tests and measures is assessed by means of the procedures belonging to the validation tradition." (Schwager, 1988, p. 38).

(iii) "Reliability, as used with respect to measurement of human performances, refers to the consistency or repeatability of measurements ( ... ). In the case of systems evaluation, valid

measurements are those that truly reflect the later performance of a system when it is in actual use." (Morgan et al., 1963, p. 49). Several reasons, as it seems, have objectively determined these issues:

(i) the lack of any agreed system or properties which have been and can be measured;

(ii) the absence of a suitable, theoretically justified and operationally feasible measurement unit;

(iii) the difficulty to fulfill, at least conditionally, the requirement of additivity;

(iv) the doubts as to the repeatability of measuring procedures when applied to the behaviour of human beings.

Further, one cannot ignore the singularity of individual

behaviour, subjective wishes, expectations, tastes, the specificity of human decisions, the disagreement of people about the relevance of their interests, the free will of man to decide even contrary to his benefit, the heterogeinity of subjective criteria for valuation influenced by a possible conflict of interests and goals. The study of human behaviour cannot be realized by procedures used in mechanics with rigid bodies. The behaviour of man is not deterministically predictabie. In short: men are not atoms.

The problem of meaningfulness which is connected with the range of the applicability of measurements, the nature of their practical execution and the expected results compared with the results actually obtained is inherently intertwined with the adopted measurement conception.

For an adherent of the broader stand-point, practically no doubts as to the meaningfulness of some procedure proclaimed as measurement will be raised as long as one can say that the numerical assignment or rather the assignment of numerals was realized "according to rule".

Somebody who defends the narrower stand-point will obviously suggest a more restricted position. To introduce some absurd examples, he will e.g. hardly agree to the meaningfulness of measuring the baldness of men in the population of Australian tailors or of the numerosity of a heap of hay.

The requirements of validity and reliability have been, I hold, introduced in connection with tests and later on extended by an

ungrounded identification of testing and measurement for various instances of extraphysical measurement. They are also

determined by various circumstances, chiefly by the fact that as measuring instruments there are applied procedures of testing and scaling (in a very broad sen se ) without clearly distinguishing whether these instruments (or rather tools, respectively

conceptual devices such as questionnaires, interviews, various testing methods) are or are not independent from the values of measured properties.

The basic decision whether such a measuring instrument is really appropriate to measure what is intended to be measured, or rather the uneasiness explicitly to say what is, in fact, measured characterizes the basic question ofvalidity: "Do we actually measure what we believe that we measure?" or "What property is by means of a given test (scale, measuring devise or technique) really measured?"

In general, it is assumed that validity is concemed with the elaboration and application of a test in respect to a directly measurable variabie and its connection with an indirectly investigated property. Contrary to the old methodological assumption, metaphorically expressed by the dictum "Natura amat simplicitatem", various authors speak - when dealing with validity - about a manifold of specifications: e.g. about content, constitutive, predicative, logical, empirical, criterion, construct, trait or nomological validity.

This annoying fact has been admitted even in the methodology of social research as follows: "In more complex situations, however, one may find that the notion of validity is misleading"(Blalock & Blalock, 1968, p. 1(0).

The requirement of validity has to secure the positive evaluation of measurement results even in spurious cases. But contrary to it, to assume that it is possible to measure a purely qualitative feature of empiricalobjects by means of indicators which are in no relevant relationship to such a property is more harmful than useful. To bring the discussion to a head, one can simply say that to speak about the validity of measurement is redundant. Either we know what we are measuring and then we have only to examine whether our procedure is appropriate to our project formulated in advance, or we do not know it and then it has no sen se to speculate about the validity problem. To claim that a test (a measure, a scale) "measures what is supposed to be measured" is misleading equally well. These devices are merely tools and are, therefore, dependent on the intentions of the user.

The requirement of reliability is due to the uncertainty of the outcome of the attempted measurement. It has been formulated because of the experiences with different values of measurement results which are exact of inexact. Also in this case the theories of reliability are "highly diverse and fragmented, using very different theoretical and statistical assumptions and procedures, and

addressing divergent issues" (Schwager, 1988, p. 40). Reliability which serves as a means to evaluate singular tests assumes that the measuring procedures are realized repeatedly under approximately same objectively controllable conditions. Only then are the numerical results comparable and can be statistically processed. Contrary to the assumption of repeatability of measurements under such conditions it is admitted, especially

in social sciences, that the possibility of repetition of tests, interviews, questionnaires is biased by the experience of people made with the assumed measuring procedure in the past, e.g. with their doubts as to the usefulness or rationality of a repeated test or interview. To require areasonabIe degree of reliability in extraphysical measurement realized by singular tests is obviously unrealistic.

Validity and reliability are sometimes associated with the theory of measurement errors. This theory developed initially in physical measurement distinguishes, as weU known, (I) random or

accidental and non-random, or systematic errors: (II) actual or true and approximate values of measured magnitudes; and (lIl) a defined, achievable and required precision of measurement results.

In extraphysical measurement, the following association between validity and reliability on one side and both types of errors on the other is suggested: Reliability is understood as "the extent of random measurement error in a measure relative to the 'true' variability in the variabie". Validity "or non-random measurement errors" is conceived as " the degree to which the measured value and the true value coincide" (Blalock & Blalock, 1982, p. 103f).

In addition to the specification it is said: " ... obviously this requires a c1ear concept of the 'true value"'.

Contrary to this view, I have again to claim, that the theory of measurement errors which among others presupposes the application of technical measurement instrurnents and the relatively unlimited repeatability of measuring procedures is hardly applicable in various attempts of extraphysical

measurement. And in respect to the notion of true value, I am glad to quote, this time, approvingly W. Schwager's view that this notion" is unwarranted on a number of grounds"(1988, p.141). It

suffices to add to this stand-point, that the tme value of magnitude is given theoretically, so to say a priori, but in behavioural and social sciences an appropriate theory of

magnitudes is completely missing. We know e.g. the tme value of the sum of the intemal angles of a triangle, but what is the tme value of the utility of a car, or of the attitude towards foreigners?

PART 111

3.1 Concretization in design

The question of how to use measurement and kindred methods in the work of designers cannot be easily answered. The complexity of designing implies a selective approach to various topics which appear to a designer relevant. This depends on the concrete task he has to realize whether in the domain of technicalor

architectural design, whether with a focus on human implications or rather on technological ones.

In designing one has to take into account a project, its feasibility, theoretical preconditions, materia! possibilities, fmancial backing, environmental consequences, usefulness, psychological and aesthetic implications, a prognosis of future effect in various directions etc. What in this multicriterial decision making can be object of measurement proper and what not? Since design embraces nearly in all instances the needs and requirements of men together with purely technical problems, a designer has to find an equilibrium between the weIl approved methods and techniques of physical measurement and quantification, and the attempts of extraphysical measurement in behavioural and socia! sciences connected with the understandable desire to obtain quantitative data. In any case he has to take into account the difference between measurement as a quantitative procedure and evaluation as a qualitative method and their mutual relationship. Evaluation is rightly considered as "one of the most hellish things a designer may be tormented with" (Vazquez & Margain, 1980, p. 218), because quantitative data themselves fulfill but an auxiliary function and their relevance depends on an evaluative interpretation in respect to the given conceptual project and its practical impacts. There has to be acknowledged, as it seems to me, a unity in diversity of quantitative and qualitative methods. The troubles of extra-physical measurement which a designer is confronted with can be exemplified by discussing the nature of utility, a property intrinsically concerned with the evaluation of partial and total outcomes of his work.

Contemporary analysis of utility, initiated by investigations of J. von Neumann and O. Morgenstem made in the framework of economics, are concerned with the expected utility theory. This theory has a very broad extent of applications: it is interpreted as a theory of normative or descriptive behaviour in decision making under risk or uncertainty, as a theory of economie behaviour of individuals, e.g. as consumers, or as a theory of preference. Today, it is usually presented in an axiomatic version. It is, principally, based on the following assumptions.

(i) lts formal framework is specified by a set ofaxioms, e.g. by the axiorns of comparability, transitivity, continuity and

independence (Chernoff-Moses, 1959, p. 8lf, 350ff). These axioms are conceived as necessary and sufficient conditions for ensuring the existence of a numerical utility function fulfilling two

properties: that of ordinal utility and that of cardinal (or measurable, expected) utility

(a) x ~ y implies u(x) ~ u(y) (b) u(px + (l-p)y)

=

pu(x) + (l-p) u(y),

where x and y are variables of different kinds (abstract utilities, desirabilities, prospects, alternatives in decision situations, options, etc.), u() the utility function, and p, (l-p) complementary

probabilities (either quantitatively determined objective probabilities according to von Neumann and Morgenstem, or qualitatively characterized subjective probabilities in systems of the Ramseyian type). It is further assumed that the utility function is unique up to any positive linear transformation. (ii) The axioms are in principle empirically significant and

verifiable in respect to the actual behaviour of rational individuals. This can be considered as the empirical basis of the given theory. (iii) lts methodological background consists in the supposition that any consistent axiomatization enables the deduction of statements concerned with numerical entities, i.e. numerical utility functions, from the accepted axioms conceived as non-numerical entities. (iv) Operationally, the values ofthe numerical utility functions have to be measurable on an interval scale or even on a ratio scale. This assumption imp lies the fulfillment of necessary conditions for the measurability on interval scales: an arbitrary scale zero, a unit and the invariance of scale form under any positive linear transformation.

These assumptions, however, are not fully fulfilled. Without going into details (cf. Berka, 1974), the following objections can be raised:

The interpretation of fonnula (b) does not satisfy the correlation between empirical and numerical notions, especially in respect to the operation px + (1-p)y which has to have an empirical character unlike the expression of its "numerical side". How to interpret the double occurrence of the sign "+"? Does it express identity or equality? Do both sides of fonnula (b) refer to the same entity, if u( ) is understood as a numerical utility function? Both properties of utility differ in respect to probability: ordinal utility is fonnulated in an unprobabilistic context unlike the probabilistic nature of expected utility.

The correctness of the axioma tic version is burdened by the following dilemma: either the fundamental theories are not rigourously deduced from the axioms (and their proof is fonnally incorrect) or the numerical utilities are already tacitly assumed in the axioms - against the presupposition that they are concemed with non-numeri cal utilities (and the derivation is

methodologically invalid).

Against the assumption that expected utility is measurable - like e.g. temperature - by means of an interval scale, it can be easily shown that neither of the three requirements for measurability on such a scale is satisfied.

(i) There has not yet been found any pseudo-unit. To add one "util" with some monetary value, e.g. one dollar, is senseless. How to compare this value with one pound or one Mark in various situations e.g. in respect to the devaluation of one currency? The intersubjective incomparability of "utilities" for different individuals points against the existence of such an "objectively" given, "constant" unit.

(ii) The scale zero, if attainable, would be on one side "more arbitrary", since the choice of quasi-numerical values assigned to the least desirabie element of some preference ordering is practically unlimited. But on the other one, it would be "more naturai" because the origin of utility sc ales would always represent the least desirabIe element of the preference order. (iii) The transfonnation fonnula for interval scales requires a significant interpretation of both constants: one represents the unit and the other one the scale zero.

The first property of utility - according to fonnula (a) - is obviously a comparative concept and can be evaluated on an ordinal scale. For cardinal utility according to fonnula (b) two

situations have to be distinguished: (i) the particular alternatives (desirabilities, options, etc.) are directly or indirectly related to objectively given quantitative data, and (ii) they have a purely qualitative nature which cannot be objectively expressed by means of quantitative data.

In the first case, caIculation can be realized in the same manner as the caIculation of mathematical expectation of the numeral data in question. For purely qualitative alternatives this possibility is excIuded. It is true, that we can assign to utilities some quasi-numerical values which would express some preference order among them. But it would be a grave mistake to handle these values as if they were numerical values and to characterize the expected utility by one unified numerical expression.

Finally, the calculation for the numeri cal values of the expected utility function depends strongly on the values of probability. Every individual can - at least ex post according to the outcome of his decision - rationalize his more or less "irrational" behaviour by a suitable subjective valuation ofhis probabilities.

My critical attitude towards expected utility theory with its consequences for the appraisal of quantification in behavioural and social sciences has shown, as I hope, many problems inherent in the broader approach to measurement. Whether the waming remarks not to overestimate the relevance of quantitative methods will be accepted by designers I cannot foresee. That a cautious standpoint in this direction seems to be advisable can be demonstrated e.g. by the following quotation.

The larger the number of distinct criteria evaluated or

measurements taken, the more information will be available on which to base an overall evaluation ( ... ) ifno one knew mileage estimates, it would be harder to evaluate a car's relative economy. Given a choice between ordinal categories such as "good", "average", "poor" and their measurement (EPA estimate), most people would prefer the number (as long as a reason exists to believe that differences between numbers are meaningful), because it contains more information, obviating and subsuming the more aggregate ordinal categories:

"( ... ) Anything can be measured experimentally as long as exactly how to take the measurements is defined" (Hayes-Roth et al., 1983, p. 248).

The common trap so characteristic for the adherents of the broader conception of measurement implicitly and explicitly

underlying the above mentioned quotation consists of an unjustified contamination of numbers and numerals resulting in an identification of pseudo- or quasi-quantification with

quantification proper. An assignment of numerals as labels analogously to letters or words unlike as names of numbers -easily neglected under the desire of a borderless extension of measurement is nothing el se than a special kind of non verbal designation.

So by the numerals "0" and "1" as scale values of a nominal scale there is nothing more expressed than by an appraisal by means of "no" and "yes", And similarly in the case of grading, the

preference ordering e.g. "excellent, very good, good, bad, very bad" fulfills the same function as the quasi-quantitative values of an ordinal scale, e.g. "1,2,3,4,5" or "1 - 0,75 - 0,5 - 0,25 - 0". A utilization of quasi-quantitative values is weIl known in valuation used in diverse sportive competitions, e.g. gymnastics or figure-skating.

Nobody will deny the advantages of the serial structure of such non-verbal expressions, i.e. numerals as simple labels only. The serial structure of numerals is, of course, fulfilled by the serial order of letters in the alphabet as weIl.

The wish to offer an "overall evaluation" operationally realized by adopting in all instances the same mathematical operations may yield disastrous results, e.g. when handling numerals always as names of numbers, and identificating then the numerall of the nominal scale with the number 1 of the ratio scale, or when adopting quasi-quantitative values of ordinal utilities in cardinal utilities and using them in calculation with numerical values of probabilities. The numerical results obtained by such a

"calculation" based on a confusion of names and objects names, nota bene in this instance conceming numerals which do not designate numbers, are evidently nonsensical.

Neither counting is free of danger to be misused by those who de sire to objectivize their investigations quantitatively. In this case, we have without any doubts to do with a quantitative method par excellence. Nevertheless, its application for any price need not be always reasonable. The demarcation between in stances of counting which seem to be useful and those which are rather extravagant is not easy to be drawn. We may aptly speak e.g. about the accident rate or birth rate, i.e. synonymously about the number of accidents or the number of bom children, expressing in the first case how many people suffered by various